Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of D9⋊H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C32 |
| direct product | C2×D9⋊H(3,𝔽3) |
| unambiguous semidirect product | D9⋊(C2×H(3,𝔽3)) |
| unambiguous semidirect product | (C2×D9)⋊H(3,𝔽3) |
| unambiguous semidirect product | (C2×C3×AGL(1,ℤ/9))⋊C3 |
| Fitting | C2×C9⋊H(3,𝔽3) ⋊ C2 |
| Sylow | C9⋊H(3,𝔽3) ⋊ C22 |
215 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 215 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | D9⋊((C3⋊Dic3)⋊C3), #14516817, #14516819, … |
| maximal normal subgroup of | D9⋊((C3⋊Dic3)⋊C3), #14516817, #14516819, … |
| maximal quotient of | Dic18⋊H(3,𝔽3), C4×D9⋊H(3,𝔽3), C4⋊(D9⋊H(3,𝔽3)), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 607);